Expand the following expression, using Binomial Theorem: from
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    Binomial Theorem

    Multiple Choice QuestionsShort Answer Type

    51. How many terms do the expansion of the following have?
    left parenthesis 1 minus 2 straight x plus straight x squared right parenthesis to the power of 7
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    52. Expand using Binomial Theorem. open parentheses 1 plus straight x over 2 minus straight x over 2 close parentheses to the power of 4 comma space straight x not equal to 0
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    Multiple Choice QuestionsLong Answer Type

    53. Find the co-efficient of x5 in the product (1 + 2x)6 (1 -x)7 using Binomial theorem.
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    54. Find the co-efficient of a4 in the product (1 + 2a)4 (2 - a)5 using Binomial Theorem. 
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    Multiple Choice QuestionsShort Answer Type

    55. Using Binomial Theorem, expand the following expression:
    <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>
    162 Views
    Answer
    56. Using Binomial Theorem, expand the following expression:
    <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>
    173 Views
    Answer
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    57. Expand the following expression, using Binomial Theorem:
    <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>

    left parenthesis 1 minus 2 straight x plus straight x squared right parenthesis cubed space equals space left parenthesis 1 minus straight x right parenthesis to the power of 6 space equals space left square bracket left parenthesis 1 right parenthesis space plus space left parenthesis negative straight x right parenthesis right square bracket to the power of 6
                          equals straight C presuperscript 6 subscript 0 left parenthesis 1 right parenthesis to the power of 6 left parenthesis negative straight x right parenthesis to the power of 0 plus straight C presuperscript 6 subscript 1 left parenthesis 1 right parenthesis to the power of 5 left parenthesis negative straight x right parenthesis to the power of 1 plus straight C presuperscript 6 subscript 2 left parenthesis 1 right parenthesis to the power of 4 left parenthesis negative straight x right parenthesis squared plus straight C presuperscript 6 subscript 3 left parenthesis 1 right parenthesis cubed left parenthesis negative straight x right parenthesis cubed
                                               space space plus straight C presuperscript 6 subscript 4 left parenthesis 1 right parenthesis squared left parenthesis negative straight x right parenthesis to the power of 4 plus straight C presuperscript 6 subscript 5 left parenthesis 1 right parenthesis to the power of 1 left parenthesis negative straight x right parenthesis to the power of 5 plus straight C presuperscript 6 subscript 6 left parenthesis 1 right parenthesis to the power of 0 left parenthesis negative straight x right parenthesis to the power of 6
                        space space space equals left square bracket left parenthesis 1 right parenthesis space left parenthesis 1 right parenthesis space left parenthesis 1 right parenthesis right square bracket plus left square bracket left parenthesis 6 right parenthesis space left parenthesis 1 right parenthesis space left parenthesis negative straight x right parenthesis right square bracket plus space left square bracket left parenthesis 15 right parenthesis space left parenthesis 1 right parenthesis space left parenthesis straight x squared right parenthesis right square bracket space plus space left square bracket left parenthesis 20 right parenthesis space left parenthesis 1 right parenthesis space left parenthesis negative straight x cubed right parenthesis right square bracket
                                                  plus left square bracket left parenthesis 15 right parenthesis space left parenthesis 1 right parenthesis space left parenthesis straight x to the power of 4 right parenthesis right square bracket space plus space left square bracket left parenthesis 16 right parenthesis space left parenthesis 1 right parenthesis space left parenthesis negative straight x to the power of 5 right parenthesis right square bracket space plus space left square bracket left parenthesis 1 right parenthesis space left parenthesis 1 right parenthesis space left parenthesis straight x to the power of 6 right parenthesis right square bracket
                            equals space 1 minus 6 straight x plus 15 straight x squared minus 20 straight x cubed plus 15 straight x to the power of 4 minus 6 straight x to the power of 5 plus straight x to the power of 6.
                      
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    58. Expand the following expression, using Binomial Theorem:
    left parenthesis 1 plus straight x plus straight x squared right parenthesis cubed
    101 Views
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    59.

    Find the co-efficient of straight x squared in the expansion of open parentheses 3 straight x minus 1 over straight x close parentheses to the power of 6.

    95 Views
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    60.

    Find the term independent of x in the expansion of open parentheses straight x squared plus 1 over straight x close parentheses to the power of 9.

    106 Views
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